Lecture 15: Derivatives; Laws for Differentiation

Name: Lecture 15: Derivatives; Laws for Differentiation
Uploaded: 2025-09-02T14:18:27Z
Duration: 1 h 19 min 41 s
Description: We define what it means for a function to be differentiable. We show that if a function is differentiable at a point, then it is also continuous. We then establish the basic algebraic laws for differentiation. Those include Leibniz’s rule, the quotient rule, and the chain rule. Once we have that, we prove Rolle’s lemma and use it to show the mean value theorem.

1:19:41

We define what it means for a function to be differentiable. We show that if a function is differentiable at a point, then it is also continuous. We then establish the basic algebraic laws for differentiation. Those include Leibniz’s rule, the quotient rule, and the chain rule. Once we have that, we prove Rolle’s lemma and use it to show the mean value theorem.